Question

A friend of yours is loudly singing a single note at 403 Hz while racing toward you at 26.3 m/s on a day when the speed of sound is 340 m/s .What frequency do you hear?What frequency does your friend hear if you suddenly start singing at 403?

Answer 1

Step-by-step explanation:

Given

Natural frequency of vibration
`f=403\ Hz`

Velocity of source
`v_s=26.3\ m/s`

Considering velocity of sound
`v=341\ m/s`

Apparent Frequency of sound is given by Doppler effect

`f'=(v+v_o)/(v-v_s)\cdot f`

where
`f=natural\ frequency`

`v=velocity\ of\ sound\ wave`

`v_o=velocity\ of\ observer`

`v_s=velocity\ of\ source`

`f'=apparent\ frequency`

here
`v_o=0`

`f'=(341)/(341-26.3)\cdot 403=437.37 Hz`

If you start singing at frequency of 403 Hz then apparent frequency to your friend

Observer is moving with 26.3 m/s and source is stationary

`f'=(v+26.3)/(v-0)\cdot 403`

`f'=(341+26.3)/(341)\cdot 403=434.08\ Hz`